Viterbi decoder method and apparatus with RI detector in servo channel

ABSTRACT

Apparatus and methods are disclosed for decoding data stored on a data storage medium. A disclosed decoding method and decoder include a radial incoherence (RI) detector that increases the probability of detecting RI and improves the decoding performance in terms of the bit error rate of the decoded signal. RI is detected by comparing an input signal to the decoder against a RI threshold value and generating a RI-type signal. The RI detector may include a filter for filtering out noise and error in the RI-type signal, an adaptive threshold unit that adjusts the RI threshold value based upon the RI-type signal, a transition-based threshold unit that adjusts the RI threshold value based upon each transition in the input signal, or a path-based threshold unit that adjusts the RI threshold value based upon a best surviving path corresponding to the input signal, in combination or alone.

CROSS REFERENCE TO RELATED APPLICATION

This application is a continuation of co-pending U.S. patent applicationSer. No. 13/601,404, filed Aug. 31, 2012, which is a continuation ofU.S. patent application Ser. No. 13/282,910, filed Oct. 27, 2011 (nowU.S. Pat. No. 8,261,172), which is a continuation of U.S. patentapplication Ser. No. 12/015,913, filed Jan. 17, 2008 (now U.S. Pat. No.8,051,365), which claims the benefit of the filing date of U.S.Provisional Application No. 60/885,297 filed Jan. 17, 2007 (nowexpired), all of which are incorporated by reference herein in theirentireties.

TECHNICAL FIELD

The present disclosure generally relates to the retrieval of data fromdata storage mediums such as magnetic disk drives. More particularly,the present disclosure relates to a system that detects the radialincoherence generated by the movement of a read/write head over thesurface of a storage medium and decodes the data stored on a datastorage medium.

BACKGROUND

A modern computing system typically comprises a central processing unit,a memory unit, and supporting hardware necessary to communicate bothwithin the system and to the outside world. Within the computing system,communication buses may exist to transmit information and instructionsbetween the processing unit and the memory unit. To communicate with theoutside world, input and output (“I/O”) devices may be used. Commonexamples of input devices include the keyboard and mouse. Output devicesinclude printers and display devices such as a monitor. In addition,storage devices such as hard disk drives, floppy disk drives, andoptical disk drives may serve as both input and output devices.

In conventional hard disk drives, information in the form of analog ordigital data is recorded on concentric tracks on a magnetic disk. Thedisk is spun at a very high speed while a read/write head moves radiallyover the surface of the disk in order to read information from or writeinformation to the tracks. Information which is read out from a disk maybe supplied to a device known as a Viterbi decoder to generate areproduction of an original data signal recorded on the disk.

One type of information commonly written to and read from the tracks isservo information. Servo information may comprise control informationsuch as address and position information to allow proper alignment ofthe read/write head with respect to the tracks, as well as other trackidentification information. Servo information is often written on aportion of the disk platter known as a servo wedge. Within a servowedge, the servo information is broken up into multiple servo fields,each typically containing a different type of servo information. Whilereading such information or performing a seek operation to pinpoint aspecific track, a read/write head may radially traverse multiple tracks.When the servo wedges are not properly aligned along the radialdirection, “radial incoherence” (RI) may result. RI is the timing offsetthat occurs when a head moves between radially adjacent tracks in whichthe servo wedges are not properly aligned. The waveform signal read bythe head may undergo a phase shift due to the RI, called the RI phase,which leads to errors in decoding the recorded servo information.

Typically, RI is detected by a RI detector with a fixed or symmetric RIdetection threshold in a servo channel. However, a RI detectionthreshold that is set too high may fail to detect RI when it exists.Conversely, a RI detection threshold that is set too low may detectfalse positives when no RI exists. In addition, noise or other errorscan corrupt a sequence of RI data.

Thus, there is a need for an improved system for RI detection thatincreases the probability of detecting RI and reduces the bit error rate(BER) of a decoded signal read from a disk.

SUMMARY

Disclosed is a system for decoding data stored on a data storage medium.The system comprises a first input terminal receiving a data stream readfrom the data storage medium. The data stream comprises a plurality ofdata transitions. The system further comprises an input unit identifyingportions of the data stream as possible transitions and selecting asubset of the possible transitions in response to a selection input. Asecond input unit generates estimated phases of the possible transitionsand selects one of the estimated phases. A phase buffer stores aplurality of the selected estimated phases. An adder generates a firstsum by adding the plurality of the selected estimated phases. The systemalso comprises a decision unit using the first sum to generate a flagindicating a type of radial incoherence associated with the data streamand a filter generating and supplying the selection input to the firstinput unit.

Further disclosed is a system for decoding data stored on a data storagemedium. The system comprises an input terminal receiving a data streamread from the data storage medium, the data stream comprising aplurality of data transitions. The system further comprises an inputunit identifying portions of the data stream as possible transitions andselecting a subset of the possible transitions in response to aselection input. A path-based input unit generates a first sum and apath-based threshold unit generates a second sum. The system alsocomprises a decision unit using the first and second sums to generate aflag indicating a type of radial incoherence associated with the datastream and a filter generating and supplying the selection input to thefirst input unit.

Also disclosed is a method for decoding data stored on a data storagemedium. The method comprises receiving a data stream read from the datastorage medium, the data stream comprising a plurality of datatransitions. The method further comprises identifying portions of thedata stream as possible transitions and selecting a subset of thepossible transitions in response to a selection input. The method alsocomprises estimating phases of the possible transitions and selectingone of the estimated phases. The method further comprises generating afirst sum by adding a plurality of the selected estimated phases. Themethod also comprises generating a plurality of flags indicating typesof radial incoherence associated with the data stream and generating theselection input from the plurality of flags.

Also disclosed is a method for decoding data stored on a data storagemedium. The method comprises receiving a data stream read from the datastorage medium, the data stream comprising a plurality of datatransitions. The method further comprises identifying portions of thedata stream as possible transitions and selecting a subset of thepossible transitions in response to a selection input. The method alsocomprises estimating phases of the possible transitions and generating afirst sum from the plurality of estimated phases. The method furthercomprises storing a plurality of path-based threshold values andgenerating a second sum from the plurality of path-based thresholdvalues. The method also comprises generating a plurality of flagsindicating types of radial incoherence associated with the data streamand generating the selection input from the plurality of flags.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this specification, show certain aspects of implementationsconsistent with the present invention and, together with thedescription, help explain some of the principles associated with theinvention. In the drawings,

FIG. 1 is a block diagram of an exemplary system environment consistentwith certain aspects related to the present invention;

FIG. 2 is a perspective view of a typical disk drive;

FIG. 3A depicts a servo information format;

FIG. 3B depicts the trajectory of a read/write head across aligned servowedges on radially adjacent tracks;

FIG. 3C depicts the trajectory of a read/write head across non-alignedservo wedges on radially adjacent tracks;

FIG. 3D is an illustration of a signal with negative RI;

FIG. 4 is a block diagram of a decoder with RI detector consistent withcertain aspects related to the present invention;

FIG. 5A is a two-state trellis diagram for a PR4 target;

FIG. 5B is a two-state trellis diagram for a MFPR4 target;

FIGS. 6A-E are modified two-state trellis diagrams for a PR4 targetconsistent with certain aspects related to the present invention;

FIGS. 7A-F are modified two-state trellis diagrams for a MFPR4 targetconsistent with certain aspects related to the present invention;

FIG. 8 is a block diagram of a decoder with RI detector and filterconsistent with certain aspects related to the present invention;

FIG. 9 is a block diagram of a decoder with RI detector and adaptivethreshold unit consistent with certain aspects related to the presentinvention;

FIG. 10 is a block diagram of a decoder with RI detector andtransition-based threshold unit consistent with certain aspects relatedto the present invention;

FIG. 11 is a block diagram of a decoder with RI detector and path-basedunit consistent with certain aspects related to the present invention;

FIGS. 12A-S illustrate the BER as a function of off-track phase shiftfor decoders with RI detectors consistent with certain aspects relatedto the present invention at various signal to noise ratios.

DETAILED DESCRIPTION

Reference will now be made in detail to the invention, examples of whichare illustrated in the accompanying drawings. The implementations setforth in the following description do not represent all theimplementations consistent with the claimed invention. Instead, they aremerely some examples consistent with the present invention. Whereverpossible, the same reference numbers will be used throughout thedrawings to refer to the same or like parts.

FIG. 1 is a block diagram of an exemplary computer system environmentconsistent with the present invention. Referring to FIG. 1, a system 20includes an I/O unit 21, a data storage device 22, a processing unit 23,and a display unit 24. I/O unit 21 interfaces with peripherals such askeyboards, cursor tracking devices, and printers to receive and transmitinformation to and from the other units. Display unit 24 generates andprovides viewable images as a result of information received via I/Ounit 21. Data storage device 22 may comprise hard disk drives, floppydisk drives, optical disk drives and/or other similar storage media.Data storage device 22 communicates with and is accessed by processingunit 23, which is the main or central processing unit for the system.Processing unit 23 communicates with data storage device 22, I/O unit21, and display unit 24 as well as with an internal memory unitconsisting of random access memory (RAM) and read-only memory (ROM) toperform standard processing functions on data received by and sentbetween the units. Processing unit 23 also accesses the data storagedevice 22, retrieving data which it decodes to reveal servo and otherinformation, while detecting the presence of RI. Alternatively, a diskcontroller unit (not shown) coupled to the data storage device 22 andprocessing unit 23 accesses the data storage device 22, retrieves data,decodes the data while detecting the presence of RI, and then transmitsthe decoded data to the processing unit 23 for further processing.

FIG. 2 shows in greater detail a perspective view of a typical diskdrive 35 within data storage device 22. Disk drive 35 includes acircular disk 36 which may consist of either a single platter or aplurality of individual platters, mounted on a spindle 37. Spindle 37 isattached to a spindle motor (not shown), which spins disk 36. Theplatters of disk 36 are formatted to contain concentric tracks 38 withinwhich information, such as servo information, may be recorded.Information may be recorded within tracks on either or both sides of theplatters of disk 36. This information may be recorded onto the disk in avariety of ways, for instance, in di-bit, tri-bit, or quad-bit encoding.Manchester code may also be used to encode the information. Whenencoding the information via di-bit code or Manchester Code, one userbit is encoded as four bits. For example, in di-bit code, a user bit 1is encoded as 1100, and a user bit 0 is encoded as 0000. In ManchesterCode, a user bit 1 is encoded as 1100, and a user bit 0 is encoded as0011.

Disk drive 35 also includes an actuator 41, which moves and controls anactuator arm 40 supporting a read/write head 39. In response to controlby actuator 41 and actuator arm 40, read/write head 39 moves in asubstantially radial direction across the concentric tracks 38, as shownby arrow 42.

FIG. 3A depicts an exemplary servo information format 50 recorded on aservo wedge on track 51. It will be understood by those skilled in theart that track 51 has been magnified to many times its actual size suchthat it appears to be a straight line, although it is actually part of acircular track. The servo wedge on track 51 is divided into servo fields52-55, the fields containing different types of servo information. Servofield 52 may contain a preamble field, which generally precedes servoinformation and includes information to identify where servo informationbegins and to synchronize timing circuits. A servo index mark (SIM) anda servo address mark (SAM) field, contained in servo field 53, typicallyfollow the preamble field and also contain identifying and synchronizinginformation. Servo field 54 may contain a Gray Code (GC) field which isgenerally encoded in Manchester Code and which includes information suchas a track and wedge identification number (track-ID) for positioningread/write head 39 over a track and a wedge. The application of GC makestwo radially adjacent track-IDs only differ in one di-bit. Because ofthe equivalent discrete-time response of the recording medium and theunderlying signal path, the GC in the read-back signal is generally inthe form of convolution code. Servo field 55 may contain a pad fieldwhich separates the GC from servo burst data (not shown). Although servoformat 50 depicts only four servo fields 52-55 with preamble, SIM andSAM, GC, and pad information, servo fields containing other types ofinformation not described here may also be used.

When playing back the servo data, it is expected that read/write head 39moves along the center of a track 51 such that the interference fromadjacent tracks will be very small and thus can be ignored. In reality,however, read/write head 39 may not always move along the center of atrack, resulting in influence from adjacent tracks that cannot beignored. In considering the influence of adjacent tracks, a linear modelis frequently used. The signal at the output of read/write head 39 maybe modeled as:z(t)=(1−α)*x(t)+α*y(t)  (1)where z(t) is the signal at the output of read/write head 39, x(t) isthe on-track (i.e., the target track) signal, y(t) is the off-track(i.e., one of the adjacent tracks) signal, and 0≦α≦1 is the position ofread/write head 39. If α=0, read/write head 39 is at the center ofon-track. If α=0.5, read/write head 39 is at the middle of the twotracks, on-track and off-track. If α=1, read/write head 39 is at thecenter of off-track.

The signal read by read/write head 39 is in the form of acontinuous-time waveform. This signal will usually pass through ananalog front end (AFE), an analog to digital converter (ADC), and adigital equalizer. The signal at the output of the digital equalizer,which is the input signal to the Viterbi decoder, may be modeled as:z′(k)=(1−α)*x′(k)+α*y′(k)  (2)where z′(k) is the signal at the output of the digital equalizer and theinput signal to the Viterbi decoder and x′(k) and y′(k) are the samplesat the equalizer output for signals x(t) and y(t), respectively, at thek-th sampling instant, where k is an integer. From Equation (2), it isevident that z′(k) will be different than the desired signal x′ (k) aslong as y′ (k)≠x′ (k) and α≠0. This effect is called RI as it is due tothe radial offset of the read/write head 39 from the center of theon-track.

An exemplary servo information format 50, servo field 54 contains atrack-ID in GC and the GC of two radially adjacent servo fields 54 in asame servo wedge only differ by one di-bit (i.e., four coded bits), andeach of the servo fields 52, 53, and 55 on a same servo wedge are thesame. Thus, the waveforms of the servo fields on a servo wedge acrossradially adjacent tracks will have the same shape. The waveforms willdiffer only in initial phase. Accordingly, y(t), the off-track signal,can be expressed as:y(t)=x(t−τ)  (3)where τ is a real value and represents the phase difference. Negative RIoccurs where τ<0 and α≠0. Positive RI occurs where τ>0 and α≠0.

FIG. 3B depicts a servo wedge on radially adjacent tracks 51 a-c, withservo fields 52-55 aligned along boundaries 61. Again, It will beunderstood by those skilled in the art that tracks 51 a-c have beenmagnified to many times their actual size such that they appear to bestraight lines, although they are actually part of circular tracks. Inthe aligned system, boundaries 61 of the servo fields in a servo wedgeon a track are aligned with the boundaries of the servo fields in theservo wedge on adjacent tracks. In an overhead, magnified view of a diskwith aligned servo wedge fields, the servo wedge fields may appear likespokes in a wheel, radiating out from the center of the disk.

FIG. 3B shows several possible trajectories 62-64 representing therelative movement of read/write head 39 (not shown). The position ofread/write head 39 relative to adjacent tracks affects the signal thatis read by the read/write head. Trajectory 63 represents the relativemovement of read/write head 39 along the center of track 51 b, wheretrack 51 b is the on-track. Because read/write head 39 is movingdirectly along the center of the track, the head picks up the strongestsignal from track 51 b. Read/write head 39 is picking up a strongon-track signal and any signals the head may sense from adjacent tracks(i.e., off-track signals) are weak. RI does not exist along path 63since the read/write head picks up a strong signal from track 51 b andnegligible signal from adjacent tracks. Also, the servo fields inadjacent tracks of the servo wedge are aligned and thus, the signalsfrom the adjacent tracks will all be in the same phase. When the signalsare all in the same phase, τ=0, there is no destructive interference,and the linear combination of the waveform signals from all the trackswhich read/write head 39 may sense will produce no RI.

Trajectory 62 represents the relative movement of read/write head 39directly between tracks 51 b and 51 c. Because of the read/write head'sposition relative to tracks 51 b and 51 c, it senses a signal from bothtracks. Though the signal that read/write head 39 picks up combines thesignals from track 51 b and 51 c, RI does not exist because the servofields in the servo wedge are aligned and there is no phase shiftbetween the signals picked up from the tracks.

Trajectory 64 represents the relative movement of read/write head 39including radial movement across tracks from track 51 b to 51 a. Asread/write head 39 moves between tracks 51 b and 51 a, the signal fromtrack 51 b grows weaker as the head moves away from the center of thetrack and the signal from track 51 a grows stronger as the head movestoward the center of track 51 a. However, RI does not exist because theservo fields are aligned, thus there is no phase shift between signalsfrom the two radially adjacent tracks. In FIG. 3B, no RI exists becausez′(k)=x′(k). This requires that α=0, as shown in trajectory 63, or thaty(t)=x(t−τ) and τ=0, as shown in trajectories 62-64.

FIG. 3C depicts a servo wedge on tracks 51 d-f with non-aligned servofields 52-55. It will be understood by those skilled in the art thattracks 51 d-f have been magnified to many times their actual size suchthat they appear to be straight lines, although they are actually partof circular tracks. Servo fields 52-55 are non-aligned along boundary75. Boundary 75 between the servo fields shifts position along the polaraxis from track 51 d to 51 e and from track 51 e to 51 f.

The relative movement of read/write head 39 is shown along differenttrajectories 70-74. Trajectory 72 represents the relative movement ofread/write head 39 along the center of track 51 e, where track 51 e isthe on-track. Because the read/write head is moving directly along thecenter of the track, the head picks up the strongest signal from track51 e. Any signals the head may sense from adjacent tracks 51 d and 51 f(i.e., off-track signals) are weak. RI does not exist along trajectory72 since read/write head 39 picks up a strong signal from track 51 e andnegligible signals from adjacent tracks. In trajectory 72, z′(k)=x′(k)because α=0.

Trajectory 70 represents the relative movement of read/write head 39directly between tracks 51 e and 51 f. Because of the read/write head'sposition relative to tracks 51 e and 51 f, it senses a signal from bothtracks. Relative to the position of the servo fields on track 51 e, theservo fields on track 51 f are farther along the polar axis in thedirection of the read/write head's relative movement. Accordingly,read/write head 39 senses a signal from track 51 f with a positive phaseshift relative to that of the signal it senses from track 51 e. Thisphase shift between the two signals causes destructive interference andthe combined signal picked up by read/write head 39 will have positiveRI. Positive RI occurs when read/write head 39 is in the middle of tworadially adjacent servo fields of a servo wedge on radially adjacenttracks. When this occurs α=0.5. Both the on-track and off-track signalshave the same shape, but the off-track signal is delayed by one codedbit cycle with respect to the on-track signal. The off-track signal canbe expressed as:y(t)=x(t−T)  (4)where T is the coded bit cycle.

Trajectory 73 represents the relative movement of read/write head 39first along the center of track 51 e and then in a radial directionacross tracks from track 51 e to 51 f. While read/write head 39 movesalong the center of track 51 e, the signal picked up by read/write head39 is the on-track signal and has no RI. As read/write head 39 movesbetween the two tracks 51 e and 51 f, the signal from track 51 e growsweaker as the head moves away from the center of the track and thesignal from track 51 f (i.e., off-track signal) grows stronger as thehead moves toward the center of track 51 f. Relative to the position ofthe servo fields on track 51 e, the servo fields on track 51 f arefarther along the polar axis in the direction of the read/write head'srelative movement. Accordingly, read/write head 39 senses a signal fromtrack 51 f with a positive phase shift relative to that of the signal itsenses from track 51 e. This phase shift between the two signals causesdestructive interference and the combined signal picked up by read/writehead 39 as it moves radially across the tracks will have positive radialincoherence.

Trajectory 71 represents the relative movement of read/write head 39moving directly between tracks 51 e and 51 d. Because of the read/writehead's position relative to tracks 51 e and 51 d, it senses a signalfrom both tracks. Relative to the position of the servo fields on track51 e, the servo fields on track 51 f are not as far along the polar axisin the direction of the read/write head's relative movement.Accordingly, read/write head 39 senses a signal from track 51 d with anegative phase shift relative to that of the signal it senses from track51 e. This phase shift between the two signals causes destructiveinterference and the combined signal picked up by read/write head 39will have negative radial incoherence. Just like positive RI, negativeRI occurs when read/write head 39 is in the middle of two radiallyadjacent servo fields of a servo wedge on radially adjacent tracks. Whenthis occurs α=0.5. Both the on-track and off-track signals have the sameshape, but the off-track signal precedes the on-track signal by onecoded bit cycle. The off-track signal can be expressed as:y(t)=x(t+T)  (4)where T is the coded bit cycle.

Trajectory 74 represents the relative movement of read/write head 39 ina radial direction across tracks from track 51 e to 51 d. As read/writehead 39 moves between the two tracks 51 e and 51 d, the signal fromtrack 51 e grows weaker as the head moves away from the center of thetrack and the signal from track 51 d grows stronger as the head movestoward the center of track 51 d. Relative to the position of the servofields on track 51 e, the servo fields on track 51 d are not as faralong the polar axis in the direction of the read/write head's relativemovement. Accordingly, read/write head 39 senses a signal from track 51d with a negative phase shift relative to that of the signal it sensesfrom 51 e. This phase shift between the two signals causes destructiveinterference and the combined signal picked up by read/write head 39 asit moves radially across the tracks will have negative radialincoherence.

FIG. 3D is a phase diagram depicting the occurrence of negative RI.Waveform 47 depicts an on-track signal. Waveform 45 depicts an off-tracksignal. And waveform 46 depicts the combination of the on-track andoff-track signals, which results in a signal with negative radialincoherence.

FIG. 4 is a block diagram of a decoder 85 including a RI detector 86,consistent with certain aspects related to the present invention.Decoder 85 may be a two-state or four-state Viterbi ormaximum-likelihood decoder and may comprise an input unit 91, anadd-compare-select (ACS) unit 94, an output unit 95, and RI detector 86.Input unit 91 may further comprise a branch metric unit 88 and a branchmetric selector 92. In addition, RI detector 86 may further comprise asecond input unit 97, a phase buffer 84, phase adder 127, and a decisionunit 100. Second input unit 97 may further comprise a phase estimator 87and a phase selector 98. It will be understood by one of skill in theart that decoder 85 may provide for more than two or four states.

Decoder 85 receives an input data stream at an input terminal 90. Inputdata stream may comprise x₀[n], x₁[n], x₂[n], and x₃[n], a user bit thatcorresponds to four coded bits and represents one transition. The inputdata stream originates as an analog signal picked up by read/write head39 (FIG. 2). The analog signal is then passed through circuitry (notshown), such as an AFE, an ADC, and a digital equalizer to produce adigital input data stream. It is expected that the overall response atthe output of the equalizer and the input of decoder 85 will match aknown target. Two typically used targets are a PR4 target and matchedfilter PR4 (MFPR4) target.

In decoding the input data stream, decoder 85 may employ a trellisdiagram, also called a state transition diagram, to determine a bitsequence most likely to have been recorded on the storage medium out ofall possible bit sequences that may have been recorded. The PR4 andMFPR4 targets use different trellis diagrams.

The PR4 target response may be expressed as:H(D)=1+0D−D ²  (5)where H(D) is a transfer function of the PR4 target and D is an integercoefficient implementing the transfer function. The PR4 target may berepresented as a vector of tap weights [2, 0, −2] where a scaling factorof 2 has been used.

Referring to FIG. 5A, a trellis diagram 110 corresponding to a PR4target is shown. Trellis diagram 110 depicts a two-state trellisbeginning at time instant t=0 and ending at time instant t=1. Eachpossible transition from a current state to a next state is depicted bya solid or dashed line and is called a branch. For example, at time t=0,branches 111 and 112 start at current state 0 and branches 113 and 114start at current state 1. Possible next states include 0 or 1 followinga next user bit of 0 or 1. The dashed lines, branches 111 and 113,represent a next user bit of 0 and the solid lines, branches 112 and114, represent a next user bit of 1.

The memory length of a PR4 target is one user bit, which corresponds tofour coded bits. Accordingly, each branch 111-114 can be represented bythe four ideal output samples that correspond to the particulartransition. The 0→0 transition shown by branch 111 may be represented as(2, 2, −2, −2). The 0→1 transition shown by branch 112 may berepresented as (2, 2, 0, 0). The 1→0 transition shown by branch 113 maybe represented as (−2, −2, 0, 0). The 1→1 transition shown by branch 114may be represented as (−2, −2, 2, 2). A path through the trellis isrepresented by a sequence of state transitions or branches over time.

The trellis diagram 110 of FIG. 5A corresponds to a PR4 target withoutRI. In FIGS. 6A-E, modified trellis diagrams accounting for different RItypes corresponding to a PR4 target are shown. In FIG. 6A, a trellisdiagram for a signal with negative RI in which the previous and futureuser bits do not matter is shown. In FIG. 6B, a trellis diagram used ina servo channel for a signal with negative RI is shown. In FIG. 6C, atrellis diagram for a signal with positive RI and a previous user bit of0 is shown. In FIG. 6D, a trellis diagram for a signal with positive RIand a previous user bit of 1 is shown. In FIG. 6E, a trellis diagramused in a servo channel for a signal with positive RI is shown.

The MFPR4 target response may be expressed as:H(D)=−1+0D+2D ²+0D ³−1D ⁴  (5)where H(D) is a transfer function of the MFPR4 target and D is aninteger coefficient implementing the transfer function. The MFPR4 targetmay be represented as a vector of tap weights [−1, 0, 2, 0, −1].

Referring to FIG. 5B, a trellis diagram 120 corresponding to a MFPR4target is shown. Trellis diagram 120 depicts a two-state trellisbeginning at time instant t=0 and ending at time instant t=1. Eachpossible transition from a current state to a next state is depicted bya solid or dashed line and is called a branch. For example, at time t=0,branches 121 and 122 start at current state 0 and branches 123 and 124start at current state 1. Possible next states include 0 or 1 followinga next user bit of 0 or 1. The dashed lines, branches 121 and 123,represent a next user bit of 0 and the solid lines, branches 122 and124, represent a next user bit of 1.

The memory length of a MFPR4 target is one user bit, which correspondsto four coded bits. Accordingly, each branch 121-124 can be representedby the four ideal output samples that correspond to the particulartransition. The 0→0 transition shown by branch 121 may be represented as(2, 2, −2, −2). The 0→1 transition shown by branch 122 may berepresented as (1, 1, 1, 1). The 1→0 transition shown by branch 123 maybe represented as (−1, −1, −1, −1). The 1→1 transition shown by branch124 may be represented as (−2, −2, 2, 2). A path through the trellis isrepresented by a sequence of state transitions or branches over time.

The trellis diagram 120 of FIG. 5B corresponds to a MFPR4 target withoutRI. In FIGS. 7A-F, modified trellis diagrams accounting for different RItypes and corresponding to a MFPR4 target are shown. In FIG. 7A, atrellis diagram for a signal with negative RI and a next user bit of 0is shown. In FIG. 7B, a trellis diagram for a signal with negative RIand a next user bit of 1 is shown. In FIG. 7C, a trellis diagram used ina servo channel for a signal with negative RI is shown. In FIG. 7D, atrellis diagram for a signal with positive RI and a previous user bit of0 is shown. In FIG. 7E, a trellis diagram for a signal with positive RIand a previous user bit of 1 is shown. In FIG. 7F, a trellis diagramused in a servo channel for a signal with positive RI is shown.

Referring again to FIG. 4, input terminal 90 supplies an input datasignal originating from read/write head 39 (FIG. 2) to input unit 91 andSecond input unit 97. From the input data stream, branch metric unit 88within input unit 91 identifies all possible transitions in the inputdata stream (i.e., all transitions in the applicable trellis diagrams)and calculates a branch metric value for each. The branch metric foreach branch represents the probability or likelihood that that branch isthe most likely transition in the input data stream. Branch metric unit88 may use a set of well-known predetermined and preprogrammedcalculations or it may use a variety of calculations adaptive to severalconditions to determine each branch metric. For instance, branch metricvalues may be calculated using Euclidean-based branch metric equations,Manhattan-based branch metric equations, or Hamming-based branch metricequations. Branch metric unit 88 may also use a set of three differenttrellis diagrams or three different sets of calculations to calculatebranch metric values for transitions not influenced by RI, transitionsinfluenced by positive RI, and transitions influenced by negative RI.

The Euclidean-based branch metrics calculations associated with eachtransition, assuming a signal with no RI, for a PR4 target may bewritten as:0→0 −2x ₀ [n]−2x ₁ [n]+2x ₂ [n]+2x ₃ [n]+8  (6)1→0 2x ₀ [n]+2x ₁ [n]+40→1 −2x ₀ [n]−2x ₁ [n]+41→1 2x ₀ [n]+2x ₁ [n]−2x ₂ [n]−2x ₃ [n]+8where x₀[n], x₁[n], x₂[n], and x₃[n] are the individual data points inthe input data stream at an n-th transition.

The Euclidean-based branch metrics calculations associated with eachtransition, assuming an input signal with negative RI, for a PR4 targetmay be written as:0→0 −2x ₀ [n]+2x[n]+4  (7)1→0 2x ₀ [n]+x ₁ [n]+2.50→1 −2x ₀ [n]−x ₁ [n]+2.51→1 2x ₀ [n]−2x ₂ [n]+4where x₀[n], x₁[n], x₂[n], and x₃[n] are the individual data points inthe input data stream at an n-th transition.

The Euclidean-based branch metrics calculations associated with eachtransition, assuming an input signal with positive RI, for a PR4 targetmay be written as:0→0 −2x ₁ [n]+2x ₃ [n]+4  (8)1→0 2x ₁ [n]+x ₂ [n]+2.50→1 −2x ₁ [n]−x ₂ [n]+2.51→1 2x ₁ [n]−2x ₃ [n]+4where x₀[n], x₁[n], x₂[n], and x₃[n] are the individual data points inthe input data stream at an n-th transition.

The Euclidean-based branch metrics calculations associated with eachtransition, assuming a signal with no RI, for a MFPR4 target may bewritten as:0→0 −2x ₀ [n]−2x ₁ [n]+2x ₂ [n]+2x ₃ [n]+8  (9)1→0 x ₀ [n]+x ₁ [n]+x ₂ [n]+x ₃ [n]+20→1 −x ₀ [n]−x ₁ [n]−x ₂ [n]−x ₃ [n]+21→1 2x ₀ [n]+2x ₁ [n]−2x ₂ [n]−2x ₃ [n]+8where x₀[n], x₁[n], x₂[n], and x₃[n] are the individual data points inthe input data stream at an n-th transition.

The Euclidean-based branch metrics calculation associated with eachtransition, assuming a signal with negative RI, for a MFPR4 target maybe written as:0→0 −2x ₀ [n]+2x ₂ [n]+4  (10)1→0 x ₀ [n]+x ₁ [n]+x ₂ [n]+1.50→1 −x ₀ [n]−x ₁ [n]−x ₂ [n]+1.51→1 2x ₀ [n]−2x ₂ [n]+4where x₀[n], x₁[n], x₂[n], and x₃[n] are the individual data points inthe input data stream at an n-th transition.

The Euclidean-based branch metrics calculations associated with eachtransition, assuming a signal with positive RI, for a MFPR4 target maybe written as:0→0 −2x ₁ [n]+2x ₃ [n]+4  (11)1→0 x ₁ [n]+x ₂ [n]+x ₃ [n]+1.50→1 −x ₁ [n]−x ₂ [n]−x ₃ [n]+1.51→1 2x ₁ [n]−2x ₃ [n]+4

where x₀[n], x₁[n], x₂[n], and x₃[n] are the individual data points inthe input data stream at an n-th transition.

Branch metric unit 88 supplies a set of branch metrics for eachidentified transition, influenced by positive RI, negative RI, and no RIto branch metric selector 92 within input unit 91. Branch metricselector 92 is coupled to branch metric unit 88 and decision unit 100within RI detector 89. From decision unit 100 branch metric selector 92receives a RI flag 101 that can be shown as RI[n−N], where n representsthe n-th input transition and N is a positive integer and represents theoverall pipeline latency with respect to the input data signal at inputterminal 90. Based on whether RI flag 101 indicates positive RI,negative RI, or no RI, branch metric selector 92 selects a correspondingsubset of transitions 93 from the transitions identified by branchmetric unit 88.

Branch metric selector 92 is coupled to ACS unit 94 and supplies subsetof transitions 93 to ACS unit 94, which determines possible survivingpaths from the transitions in subset of transitions 93. The possiblesurviving paths evolve from previously determined surviving paths. Thepath metric value for each possible surviving path is calculated usingthe branch metric of each transition in subset of transitions 93 and thepath metric values of previously determined surviving paths, where thepath metric values for the previously determined surviving paths arestored in PM0 107 and PM1 108 in output unit 95. Comparing the pathmetric values for each possible surviving path merging at a same state,ACS unit 94 determines a surviving path associated with each trellisstate. The path metric for the surviving paths are stored in PM0 107 andPM1 108 in output unit 95. This is equivalent to extending eachpreviously determined surviving path by adding one new branch to it,where the newly added branches are selected from subset of transitions93. ACS unit 94 then compares the path metrics for the surviving pathsto determine a best surviving path. ACS unit 94 selects a most recenttransition in the best surviving path, a selected transition 96, whichis one of the newly added branches. Selected transition 96 is suppliedto output unit 95 and also to phase selector 98 within second input unit97.

ACS unit 94 is coupled to output unit 95 and supplies the path metricvalue for the surviving path associated with each trellis state, thenewly added branches, the best surviving path, and selected transition96 to output unit 95. PM0 107 in output unit 95 stores the path metricvalue for the surviving path associated with state 0. PM1 108 in outputunit 95 stores the path metric value for the surviving path associatedwith state 1. Access and operation control unit (control unit) 109 mayextend the previously determined surviving paths stored in path buffers125 and 126 by first shuffling them based on the path metric value forthe surviving path associated with each trellis state and then adding,at the end of the previously determined surviving paths, the newlydetermined branches. Control unit 109 keeps track of the best survivingpath.

Output unit 95 may also compare a plurality of subset of transitions 93and a plurality of selected transitions 96, the best surviving path, togenerate a decoded data signal 104. For instance, using the bestsurviving path and its path metric value, output unit 95 may followevery transition in the best surviving path from a current timebackwards to a fixed trace depth to determine the correctness of thebest surviving path calculated by ACS unit 94. Output unit 95 thenconstructs a corrected best surviving path from which it outputs adecoded data signal 104.

Input terminal 90 also supplies second input unit 97, within RI detector86, with the input data stream. Phase estimator 87 within second inputunit 97 generates an estimated phase from the input data stream for eachpossible transition within the input data stream. For example, given thetwo states 0 and 1, phase estimator 87 generates phase estimates for thefollowing four transitions: 0→0; 0→1; 1→0; and 1→1. Like branch metricunit 88, phase estimator 87 may use a set of well-known predeterminedand preprogrammed calculations or it may use a variety of calculationsadaptive to several conditions to generate the estimated phase for eachtransition.

The RI phase associated with each transition for a PR4 target may beestimated by using:0→0 (−x ₀ [n]+x ₁ [n]+x ₂ [n]−x ₃ [n])/wt12  (12)1→0 (x ₀ [n]−x ₁ [n])/20→1 (x ₁ [n]−x ₀ [n])/21→1 (x ₀ [n]−x ₁ [n]+x ₃ [n]−x ₂ [n])/wt12where x₀[n], x₁[n], x₂[n], and x₃[n] are the individual data points inthe input data stream at an n-th transition and wt12 is a scaling factorused to balance the estimated phase and its variance for differenttransitions.

The RI phase associated with each transition for a MFPR4 target may beestimated by using:0→0 (−x ₀ [n]+x ₁ [n]+x ₂ [n]−x ₃ [n])/wt12  (13)1→0 x ₀ [n]−x ₃ [n]0→1 x ₀ [n]+x ₃ [n]1→1 (x ₀ [n]−x ₁ [n]−x ₂ [n]+x ₃ [n])/wt12where x₀[n], x₁[n], x₂[n], and x₃[n] are the individual data points inthe input data stream at an n-th transition and wt12 is a scaling factorused to balance the estimated phase and its variance for differenttransitions.

Phase estimator 87 supplies the generated estimated phases to phaseselector 98 within second input unit 97. Phase selector 98 also receivesselected transition 96 from ACS unit 94 or output unit 95. In responseto selected transition 96, phase selector 98 selects an estimated phase99.

Phase selector 98 supplies selected estimated phase 99 to phase buffer84. Phase buffer 84 is coupled to phase selector 98 and phase adder 127.Phase buffer 84 receives and stores the M most recent values of selectedestimated phase 99, where M is a positive integer. The larger the valueof M, the more any noise in the input data signal will be compressed.However, the larger the value of M, the slower the response of decoder85 and RI detector 86 to a RI type change. Phase buffer 84 sends the Mmost recent values of selected estimated phase 99 to phase adder 127.

Phase adder 127 calculates a moving sum ph_sum[n] 128 of the M mostrecent values of selected estimated phase 99 from the phase buffer 84.Decision unit 100 receives ph_sum[n] 128 from phase adder 127. Decisionunit 100 may use a fixed threshold value, a set of fixed thresholdvalues, or other ways of obtaining a detection threshold valueconsistent with the present invention to determine whether RI exists andif so, whether it is positive or negative. For example, decision unit100 may compare the value of ph_sum[n] 128 against two present thresholdvalues, −THR and +THR, to determine whether there exists positive RI,negative RI, or no RI. Based on the comparison, decision unit 100generates RI flag 101, which indicates positive RI, negative RI, or noRI. Decision unit 100 supplies RI flag 101 to branch metric selector 92within input unit 91. Object 102 between decision unit 100 and branchmetric selector 92 is merely illustrative of the overall pipelinelatency N with respect to the input data signal at input terminal 90.

FIG. 8 is a block diagram of a decoder 80 different from decoder 85 ofFIG. 4. Decoder 80 includes a RI detector 89 having filter 105,consistent with certain aspects related to the present invention.Decoder 80 may be a two-state or four-state Viterbi ormaximum-likelihood decoder and may comprise input unit 91, ACS unit 94,output unit 95, and RI detector 89. Input unit 91 may further comprisebranch metric unit 88 and branch metric selector 92. In addition, RIdetector 89 may further comprise second input unit 97, phase buffer 84,phase adder 127, decision unit 100, and filter 105. Second input unit 97may further comprise phase estimator 87 and phase selector 98. It willbe understood by one of skill in the art that decoder 80 may provide formore than two or four states.

Decoder 80 receives an input data stream conditioned in accordance witha PR4 or MFPR4 target, as previously described, at an input terminal 90.In decoding the input data stream, decoder 80 may employ trellisdiagrams, as shown in FIGS. 5A, 5B, 6A-6E, and 7A-7F, to determine a bitsequence most likely to have been recorded on the storage medium out ofall possible bit sequences that may have been recorded.

Referring again to FIG. 8, input terminal 90 supplies an input datasignal originating from read/write head 39 (FIG. 2) to input unit 91 andsecond input unit 97. From the input data stream, branch metric unit 88within input unit 91 identifies all possible transitions in the inputdata stream (i.e., all transitions in the applicable trellis diagrams)and calculates a branch metric value for each. The branch metric foreach branch represents the probability or likelihood that that branch isthe most likely transition in the input data stream. Branch metric unit88 may use a set of well-known predetermined and preprogrammedcalculations or it may use a variety of calculations adaptive to severalconditions to determine each branch metric. For instance, branch metricvalues may be calculated using Euclidean-based branch metric equations,Manhattan-based branch metric equations, or Hamming-based branch metricequations. Branch metric unit 88 may also use a set of three differenttrellis diagrams or three different sets of calculations to calculatebranch metric values for transitions not influenced by RI, transitionsinfluenced by positive RI, and transitions influenced by negative RI, asdescribed above in connection with Equations (6)-(11).

Branch metric unit 88 supplies a set of branch metrics for eachidentified transition, influenced by positive RI, negative RI, and no RIto branch metric selector 92 within input unit 91. Branch metricselector 92 is coupled to branch metric unit 88 and filter 105 within RIdetector 89. From filter 105, branch metric selector 92 receives a RItype signal 106. Based on whether RI type signal 106 indicates positiveRI, negative RI, or no RI, branch metric selector 92 selects acorresponding subset of transitions 93 from the transitions identifiedby branch metric unit 88.

Branch metric selector 92 is coupled to ACS unit 94 and supplies subsetof transitions 93 to ACS unit 94, which determines possible survivingpaths from the transition in subset of transitions 93. The possiblesurviving paths evolve from previously determined surviving paths. Thepath metric value for each possible surviving path is calculated usingthe branch metric of each transition in subset of transitions 93 and thepath metric values of previously determined surviving paths, where thepath metric values for the previously determined surviving paths arestored in output unit 95. Comparing the path metric values for eachpossible surviving path merging at a same state, ACS unit 94 determinesa surviving path associated with each trellis state. The path metric forthe surviving paths are stored in output unit 95. This is equivalent toextending each previously determined surviving path by adding one newbranch to it, where the newly added branches are selected from subset oftransitions 93. ACS unit 94 then compares the path metrics for thesurviving paths to determine a best surviving path. ACS unit 94 selectsa most recent transition in the best surviving path, a selectedtransition 96, which is one of the newly added branches. Selectedtransition 96 is supplied to output unit 95 and also to phase selector98 within second input unit 97.

ACS unit 94 is coupled to output unit 95 and supplies the path metricvalue for the surviving path associated with each trellis state, thenewly added branches, the best surviving path, and selected transition96 to output unit 95. As described above, output unit 95 may extend thepreviously determined surviving paths and may also generate a decodeddata signal 104.

Input terminal 90 also supplies second input unit 97, within RI detector89, with the input data stream. Phase estimator 87 within second inputunit 97 generates an estimated phase from the input data stream for eachpossible transition within the input data stream. For example, given thetwo states 0 and 1, phase estimator 87 generates phase estimates for thefollowing four transitions: 0→0; 0→1; 1→0; and 1→1. Like branch metricunit 88, phase estimator 87 may use a set of well-known predeterminedand preprogrammed calculations or it may use a variety of calculationsadaptive to several conditions to generate the estimated phase for eachtransition. Phase estimator 87 may also estimate the phase associatedwith each transition using Equations (12) and (13), as described above.

Phase estimator 87 supplies the generated estimated phases to phaseselector 98 within second input unit 97. Phase selector 98 also receivesselected transition 96 from ACS unit 94. In response to selectedtransition 96, phase selector 98 selects an estimated phase 99.

Phase selector 98 supplies selected estimated phase 99 to phase buffer84. Phase buffer 84 is coupled to phase selector 98 and phase adder 127.Phase buffer 84 receives and stores the M most recent values of selectedestimated phase 99, where M is a positive integer. The larger the valueof M, the more any noise in the input data signal will be compressed.However, the larger the value of M, the slower the response of decoder80 and RI detector 89 to a RI type change. Phase buffer 84 sends the Mmost recent values of selected estimated phase 99 to phase adder 127.

Phase adder 127 calculates a moving sum ph_sum[n] 128 of the M mostrecent values of selected estimated phase 99 from the phase buffer 84.Decision unit 100 receives ph_sum[n] 128 from phase adder 127. Decisionunit 100 may use a fixed threshold value, a set of fixed thresholdvalues, or other ways of obtaining a detection threshold valueconsistent with certain aspects related to the present invention todetermine whether RI exists and if so, whether it is positive ornegative. For example, decision unit 100 may compare the value ofph_sum[n] 128 against two present threshold values, −THR and +THR, todetermine whether there exists positive RI, negative RI, or no RI. Basedon the comparison, decision unit 100 generates RI flag 101, whichindicates positive RI, negative RI, or no RI. Decision unit 100 suppliesRI flag 101 to filter 105. Object 102 between decision unit 100 andfilter 105 is merely illustrative of the overall pipeline latency N withrespect to the input data signal at input terminal 90.

Decision unit 100 supplies RI flag 101 to filter 105. Filter 105 iscoupled between decision unit 100 and branch metric selector 92 tofilter out noise or other errors which may distort or affect the RIflag. Assuming noise and other errors do not occur in burst, filter 105corrects the error. For instance, RI flags within a sequence of RI flagsstored in filter 105 or a separate buffer (not shown) may indicatepositive RI at a series of discrete time instants, indicate no RI atanother time instant, and then again indicate positive RI at a series ofdiscrete time instants (ex. {1, 1, 1, 1, 1, 0, 1, 1, 1, 1}) due toerror, noise, or other factors causing distortion of the RI flags.Filter 105 detects and corrects for such noise and error, generating aRI type signal 106, which may have values of 1, 0, and −1. In the aboveexample, RI type signal 106 would be “1.” Filter 105 may be a non-linearfilter such as a median filter. A separate buffer (not shown) forstoring the sequence of RI flags may also be used by filter 105. In thepresent embodiment, filter 105 receives RI flags and stores a sequenceof RI flags, compares the flags in the sequence, and generates a RI typesignal 106 based upon the comparison. RI type signal 106 is thensupplied to the branch metric selector 92 within input unit 91.

FIG. 9 is a block diagram of a decoder 135 different from decoder 85 ofFIG. 4 and decoder 80 of FIG. 8. Decoder 135 includes a RI detector 130having an adaptive threshold unit 131 consistent with certain aspectsrelated to the present invention, but does not include filter 105 ofdecoder 80 (FIG. 4). Decoder 135 may be a two-state or four-stateViterbi or maximum-likelihood decoder and may comprise input unit 91,ACS unit 94, output unit 95, and RI detector 130. Input unit 91 mayfurther comprise a branch metric unit 88 and a branch metric selector92. In addition, RI detector 130 may further comprise second input unit97, phase buffer 84, phase adder 127, a decision unit 133 different fromdecision unit 100, and adaptive threshold unit 131. Second input unit 97may further comprise phase estimator 87 and phase selector 98. It willbe understood by one of skill in the art that decoder 135 may providefor more than two or four states.

Decoder 135 receives an input data stream conditioned in accordance witha PR4 or MFPR4 target, as previously described, at an input terminal 90.In decoding the input data stream, decoder 135 may employ trellisdiagrams, as shown in FIGS. 5A, 5B, 6A-6E, and 7A-7F, to determine a bitsequence most likely to have been recorded on the storage medium out ofall possible bit sequences that may have been recorded.

Referring again to FIG. 9, input terminal 90 supplies an input datasignal originating from read/write head 39 (FIG. 2) to input unit 91 andsecond input unit 97. From the input data stream, branch metric unit 88within input unit 91 identifies all possible transitions in the inputdata stream (i.e., all transitions in the applicable trellis diagrams)and calculates a branch metric value for each. The branch metric foreach branch represents the probability or likelihood that that branch isthe most likely transition in the input data stream. Branch metric unit88 may use a set of well-known predetermined and preprogrammedcalculations or it may use a variety of calculations adaptive to severalconditions to determine each branch metric. For instance, branch metricvalues may be calculated using Euclidean-based branch metric equations,Manhattan-based branch metric equations, or Hamming-based branch metricequations. Branch metric unit 88 may also use a set of three differenttrellis diagrams or three different sets of calculations to calculatebranch metric values for transitions not influenced by RI, transitionsinfluenced by positive RI, and transitions influenced by negative RI, asdescribed above in connection with Equations (6)-(11).

Branch metric unit 88 supplies a set of branch metrics for eachidentified transition, influenced by positive RI, negative RI, and no RIto branch metric selector 92 within input unit 91. Branch metricselector 92 is coupled to branch metric unit 88 and decision unit 133within RI detector 135. From decision unit 133, branch metric selector92 receives a RI flag 101. Based on whether RI flag 101 indicatespositive RI, negative RI, or no RI, branch metric selector 92 selects acorresponding subset of transitions 93 from the transitions identifiedby branch metric unit 88.

Branch metric selector 92 is coupled to ACS unit 94 and supplies subsetof transitions 93 to ACS unit 94, which determines possible survivingpaths from the transition in subset of transitions 93. The possiblesurviving paths evolve from previously determined surviving paths. Thepath metric value for each possible surviving path is calculated usingthe branch metric of each transition in subset of transitions 93 and thepath metric values of previously determined surviving paths, where thepath metric values for the previously determined surviving paths arestored in output unit 95. Comparing the path metric values for eachpossible surviving path merging at a same state, ACS unit 94 determinesa surviving path associated with each trellis state. The path metric forthe surviving paths are stored in output unit 95. This is equivalent toextending each previously determined surviving path by adding one newbranch to it, where the newly added branches are selected from subset oftransitions 93. ACS unit 94 then compares the path metrics for thesurviving paths to determine a best surviving path. ACS unit 94 selectsa most recent transition in the best surviving path, a selectedtransition 96, which is one of the newly added branches. Selectedtransition 96 is supplied to output unit 95 (not shown) and also tophase selector 98 within second input unit 97.

ACS unit 94 is coupled to output unit 95 and supplies the path metricvalue for the surviving path associated with each trellis state, thenewly added branches, the best surviving path, and selected transition96 to output unit 95. As described above, output unit 95 may extend thepreviously determined surviving paths and may also generate a decodeddata signal 104.

Input terminal 90 also supplies second input unit 97, within RI detector130, with the input data stream. Phase estimator 87 within second inputunit 97 generates an estimated phase from the input data stream for eachpossible transition within the input data stream. For example, given thetwo states 0 and 1, phase estimator 87 generates phase estimates for thefollowing four transitions: 0→0; 0→1; 1→0; and 1→1. Like branch metricunit 88, phase estimator 87 may use a set of well-known predeterminedand preprogrammed calculations or it may use a variety of calculationsadaptive to several conditions to generate the estimated phase for eachtransition. Phase estimator 87 may also estimate the phase associatedwith each transition using Equations (12) and (13), as described above.

Phase estimator 87 supplies the generated estimated phases to phaseselector 98 within second input unit 97. Phase selector 98 also receivesselected transition 96 from ACS unit 94. In response to selectedtransition 96, phase selector 98 selects an estimated phase 99.

Phase selector 98 supplies selected estimated phase 99 to phase buffer84. Phase buffer 84 is coupled to phase selector 98 and phase adder 127.Phase buffer 84 receives and stores the M most recent values of selectedestimated phase 99, where M is a positive integer. The larger the valueof M, the more any noise in the input data signal will be compressed.However, the larger the value of M, the slower the response of decoder135 and RI detector 130 to a RI type change. Phase buffer 84 sends the Mmost recent values of selected estimated phase 99 to phase adder 127.

Phase adder 127 calculates a moving sum ph_sum[n] 128 of the M mostrecent values of selected estimated phase 99 from the phase buffer 84.Decision unit 133 receives ph_sum[n] 128 from phase adder 127. Decisionunit 133 is coupled to phase adder 127, adaptive threshold unit 131, andbranch metric selector 92. Decision unit 133 also receives an adaptivethreshold value 132 from adaptive threshold unit 131. Ph_sum[n] 128 iscompared against adaptive threshold value 132 to determine whether thereexists positive RI, negative RI, or no RI. Based on the comparison,decision unit 133 generates RI flag 101, which indicates positive RI,negative RI, or no RI. Decision unit 133 supplies RI flag 101 to branchmetric selector 92 and adaptive threshold unit 131. Object 102 betweendecision unit 133 and branch metric selector 92 and adaptive thresholdunit 131 is merely illustrative of the overall pipeline latency N withrespect to the input data signal at input terminal 90.

Adaptive threshold unit 131 is coupled to decision unit 133 and suppliesadaptive threshold value 132 to decision unit 133. Adaptive thresholdunit 131 adjusts adaptive threshold value 132 as information is gainedabout the RI in the system from RI flag 101. For instance, when positiveor negative RI exists, a conventional threshold value may fail to detectwhen RI exists if it is too high. And when no RI exists, conventionalthreshold value may detect false positives if it is too low. Thus,adaptive threshold unit 131 may output a predetermined adaptivethreshold value 132 when no information exists about RI in the system orRI flag 101 is empty. When RI flag 101 indicates no RI, adaptivethreshold unit 131 may increase adaptive threshold value 132. To achievethis result, adaptive threshold unit 131 may multiply adaptive thresholdvalue 132 by λ_(H), where λ_(H) is a parameter of adaptive thresholdunit 131. When RI flag 101 indicates positive or negative RI, adaptivethreshold unit 131 may decrease adaptive threshold value 132. To achievethis result, adaptive threshold unit 131 may multiply adaptive thresholdvalue 132 by λ₁, where λ₁ is a parameter of adaptive threshold unit 131.In the present embodiment, adaptive threshold unit 131 stores anadaptive threshold value 132, receives RI flag 101, compares RI flag 101with the adaptive threshold value 132, adjusts the adaptive thresholdvalue based upon the comparison, supplies the adjusted adaptivethreshold value to decision unit 133, and stores the adjusted adaptivethreshold value as the adaptive threshold value.

FIG. 10 is a block diagram of a decoder 160 different from decoders 85,80, and 135. Decoder 160 includes a RI detector 140 having atransition-based threshold unit 141 consistent with certain aspectsrelated to the present invention and does not include filter 105 ofdecoder 80 (FIG. 8) or adaptive threshold unit 131 of decoder 135 (FIG.9). Decoder 160 may be a two-state or four-state Viterbi ormaximum-likelihood decoder and may comprise input unit 91, ACS unit 94,output unit 95, and RI detector 140. Input unit 91 may further comprisebranch metric unit 88 and branch metric selector 92. In addition, RIdetector 140 may further comprise second input unit 97, phase buffer 84,phase adder 127, transition-based threshold unit 141, and a decisionunit 151 different from decision units 100 and 133. Second input unit 97may further comprise phase estimator 87 and phase selector 98.Transition-based threshold unit 141 may further comprise a thresholdtable 142, a threshold buffer 143, and a threshold adder 144. It will beunderstood by one of skill in the art that decoder 160 may provide formore than two or four states.

Decoder 160 receives an input data stream conditioned in accordance witha PR4 or MFPR4 target, as previously described, at an input terminal 90.In decoding the input data stream, decoder 160 may employ trellisdiagrams, as shown in FIGS. 5A, 5B, 6A-6E, and 7A-7F, to determine a bitsequence most likely to have been recorded on the storage medium out ofall possible bit sequences that may have been recorded.

Referring again to FIG. 10, input terminal 90 supplies an input datasignal originating from read/write head 39 (FIG. 2) to input unit 91 andsecond input unit 97. From the input data stream, branch metric unit 88within input unit 91 identifies all possible transitions in the inputdata stream (i.e., all transitions in the applicable trellis diagrams)and calculates a branch metric value for each. The branch metric foreach branch represents the probability or likelihood that that branch isthe most likely transition in the input data stream. Branch metric unit88 may use a set of well-known predetermined and preprogrammedcalculations or it may use a variety of calculations adaptive to severalconditions to determine each branch metric. For instance, branch metricvalues may be calculated using Euclidean-based branch metric equations,Manhattan-based branch metric equations, or Hamming-based branch metricequations. Branch metric unit 88 may also use a set of three differenttrellis diagrams or three different sets of calculations to calculatebranch metric values for transitions not influenced by RI, transitionsinfluenced by positive RI, and transitions influenced by negative RI, asdescribed above in connection with Equations (6)-(11).

Branch metric unit 88 supplies a set of branch metrics for eachidentified transition, influenced by positive RI, negative RI, and no RIto branch metric selector 92 within input unit 91. Branch metricselector 92 is coupled to branch metric unit 88 and decision unit 151within RI detector 140. From decision unit 151, branch metric selector92 receives RI flag 101. Based on whether RI flag 101 indicates positiveRI, negative RI, or no RI, branch metric selector 92 selects acorresponding subset of transitions 93 from the transitions identifiedby branch metric unit 88.

Branch metric selector 92 is coupled to ACS unit 94 and supplies subsetof transitions 93 to ACS unit 94, which determines possible survivingpaths from the transition in subset of transitions 93. The possiblesurviving paths evolve from previously determined surviving paths. Thepath metric value for each possible surviving path is calculated usingthe branch metric of each transition in subset of transitions 93 and thepath metric values of previously determined surviving paths, where thepath metric values for the previously determined surviving paths arestored in output unit 95. Comparing the path metric values for eachpossible surviving path merging at a same state, ACS unit 94 determinesa surviving path associated with each trellis state. The path metric forthe surviving paths are stored in output unit 95. This is equivalent toextending each previously determined surviving path by adding one newbranch to it, where the newly added branches are selected from subset oftransitions 93. ACS unit 94 then compares the path metrics for thesurviving paths to determine a best surviving path. ACS unit 94 selectsa most recent transition in the best surviving path, a selectedtransition 96, which is one of the newly added branches. Selectedtransition 96 is supplied to output unit 95 (not shown) and also tophase selector 98 within second input unit 97.

ACS unit 94 is coupled to output unit 95 and supplies the path metricvalue for the surviving path associated with each trellis state, thenewly added branches, the best surviving path, and selected transition96 to output unit 95. As described above, output unit 95 may extend thepreviously determined surviving paths and may also generate a decodeddata signal 104.

Input terminal 90 also supplies second input unit 97, within RI detector140, with the input data stream. Phase estimator 87 within second inputunit 97 generates an estimated phase from the input data stream for eachpossible transition within the input data stream. For example, given thetwo states 0 and 1, phase estimator 87 generates phase estimates for thefollowing four transitions: 0→0; 0→1; 1→0; and 1→1. Like branch metricunit 88, phase estimator 87 may use a set of well-known predeterminedand preprogrammed calculations or it may use a variety of calculationsadaptive to several conditions to generate the estimated phase for eachtransition. Phase estimator 87 may also estimate the phase associatedwith each transition using Equations (12) and (13), as described above.

Phase estimator 87 supplies the generated estimated phases to phaseselector 98 within second input unit 97. Phase selector 98 also receivesselected transition 96 from ACS unit 94. In response to selectedtransition 96, phase selector 98 selects an estimated phase 99.

Phase selector 98 supplies selected estimated phase 99 to phase buffer84. Phase buffer 84 receives and stores the M most recent values ofselected estimated phase 99, where M is a positive integer. The largerthe value of M, the more any noise in the input data signal will becompressed. However, the larger the value of M, the slower the responseof decoder 160 and RI detector 140 to a RI type change. Phase buffer 84sends the M most recent values of selected estimated phase 99 to phaseadder 127. Phase adder 127 calculates a moving sum ph_sum[n] 128 of theM most recent values of selected estimated phase 99 from the phasebuffer 84.

Concurrently, threshold table 142 receives selected transition 96 fromACS unit 94. Threshold table 142 contains transition-based thresholdvalues for all possible transition. The transition-based threshold valuefor each transition is one half of the average value of the absolutevalues of the ideal RI phases for that transition under both negativeand positive RI. Threshold table 142 may hold different values for thetransition-based threshold under a PR4 target and under a MFPR4 target.Threshold buffer 143 within transition-based threshold unit 141 receivesand stores the M most recent transition-based threshold valuescorresponding to selected transitions 96 from threshold table 142. The Mmost recent transition-based threshold values corresponding to selectedtransitions 96 are sent to threshold adder 144. Threshold adder 144calculates a moving sum Thr_sum[n] 145 of the M most recenttransition-based threshold values corresponding to selected transitions96.

Decision unit 151 is coupled to phase adder 127 and threshold adder 144and receives ph_sum[n] 128 and Thr_sum[n] 145. Decision unit 151compares ph_sum[n] 128 against −Thr_sum[n] 145 and +Thr_sum[n] 145 todetermine whether there exists positive RI, negative RI, or no RI. Basedon the comparison, decision unit 151 generates RI flag 101, whichindicates positive RI, negative RI, or no RI. Decision unit 151 suppliesRI flag 101 to branch metric selector 92. Object 102 between decisionunit 151 and branch metric selector 92 is merely illustrative of theoverall pipeline latency N with respect to the input data signal atinput terminal 90.

FIG. 11 is a block diagram of a decoder 180 different from decoders 85,80, 135, and 160. Decoder 180 includes a RI detector 181 having apath-based threshold unit 182 consistent with certain aspects related tothe present invention and does not include filter 105 of decoder 80(FIG. 8), adaptive threshold unit 131 of decoder 135 (FIG. 9), ortransition-based threshold unit 141 of decoder 160 (FIG. 10). Decoder180 may be a two-state or four-state Viterbi or maximum-likelihooddecoder and may comprise input unit 91, ACS unit 94, output unit 95, andRI detector 181. Input unit 91 may further comprise a branch metric unit88 and a branch metric selector 92. In addition, RI detector 181 mayfurther comprise a path-based input unit 183, a path-based thresholdunit 182, and a decision unit 184 different from decision units 100,133, and 151. Path-based input unit 183 may further comprise phaseestimator 87, a path-based phase buffer 186, and a phase calculationunit 187. Path-based threshold unit 182 may further comprise a thresholdtable 188 different from threshold table 142 and a threshold calculationunit 189. It will be understood by one of skill in the art that decoder180 may provide for more than two or four states.

Decoder 180 receives an input data stream conditioned in accordance witha PR4 or MFPR4 target, as previously described, at an input terminal 90.In decoding the input data stream, decoder 180 may employ trellisdiagrams, as shown in FIGS. 5A, 5B, 6A-6E, and 7A-7F, to determine a bitsequence most likely to have been recorded on the storage medium out ofall possible bit sequences that may have been recorded.

Referring again to FIG. 11, input terminal 90 supplies an input datasignal originating from read/write head 39 (FIG. 2) to input unit 91 andpath-based input unit 183. From the input data stream, branch metricunit 88 within input unit 91 identifies all possible transition in theinput data stream (i.e., all transitions in the applicable trellisdiagrams) and calculates a branch metric value for each. The branchmetric for each branch represents the probability or likelihood thatthat branch is the most likely transition in the input data stream.Branch metric unit 88 may use a set of well-known predetermined andpreprogrammed calculations or it may use a variety of calculationsadaptive to several conditions to determine each branch metric. Forinstance, branch metric values may be calculated using Euclidean-basedbranch metric equations, Manhattan-based branch metric equations, orHamming-based branch metric equations. Branch metric unit 88 may alsouse a set of three different trellis diagrams or three different sets ofcalculations to calculate branch metric values for transitions notinfluenced by RI, transitions influenced by positive RI, and transitionsinfluenced by negative RI, as described above in connection withEquations (6)-(11).

Branch metric unit 88 supplies a set of branch metrics for eachidentified transition, influenced by positive RI, negative RI, and no RIto branch metric selector 92 within input unit 91. Branch metricselector 92 is coupled to branch metric unit 88 and decision unit 184within RI detector 181. From decision unit 184, branch metric selector92 receives RI flag 101. Based on whether RI flag 101 indicates positiveRI, negative RI, or no RI, branch metric selector 92 selects acorresponding subset of transitions 93 from the transitions identifiedby branch metric unit 88.

Branch metric selector 92 is coupled to ACS unit 94 and supplies subsetof transitions 93 to ACS unit 94, which determines possible survivingpaths from the transitions in subset of transitions 93. The possiblesurviving paths evolve from previously determined surviving paths. Thepath metric value for each possible surviving path is calculated usingthe branch metric of each transition in subset of transitions 93 and thepath metric values of previously determined surviving paths, where thepath metric values for the previously determined surviving paths arestored in PM0 107 and PM1 108 in output unit 95. Comparing the pathmetric values for each possible surviving path merging at a same state,ACS unit 94 determines a surviving path associated with each trellisstate. The path metric for the surviving paths are stored in PM0 107 andPM1 108 in output unit 95. This is equivalent to extending eachpreviously determined surviving path by adding one new branch to it,where the newly added branches are selected from subset of transitions93. ACS unit 94 then compares the path metrics for the surviving pathsto determine a best surviving path. ACS unit 94 selects a most recenttransition in the best surviving path, a selected transition 96, whichis one of the newly added branches. Selected transition 96 is suppliedto output unit 95.

ACS unit 94 is coupled to output unit 95 and supplies the path metricvalue for the surviving path associated with each trellis state, thenewly added branches, the best surviving path, and selected transition96 to output unit 95. PM0 107 in output unit 95 stores the path metricvalue for the surviving path associated with state 0. PM1 108 in outputunit 95 stores the path metric value for the surviving path associatedwith state 1. Access and operation control unit (control unit) 109 mayextend the previously determined surviving paths stored in path buffers125 and 126 by first shuffling them based on the path metric value forthe surviving path associated with each trellis state and then adding,at the end of the previously determined surviving paths, the newlydetermined branches. Control unit 109 keeps track of the best survivingpath.

Output unit 95 may also compare a plurality of subset of transitions 93and a plurality of selected transitions 96, the best surviving path, togenerate a decoded data signal 104. For instance, using the bestsurviving path and its path metric value, output unit 95 may followevery transition in the best surviving path from a current timebackwards to a fixed trace depth to determine the correctness of thebest surviving path calculated by ACS unit 94. Output unit 95 thenconstructs a corrected best surviving path from which it outputs adecoded data signal 104. Output unit 95 is coupled to thresholdcalculation unit 189 within path-based threshold unit 182 and phasecalculation unit 187 within path-based input unit 183 via link 190.Output unit 95 may send best surviving path information to thresholdcalculation unit 182 and phase calculation unit 187 via link 190.

Input terminal 90 also supplies path-based input unit 183, within RIdetector 181, with the input data stream. Phase estimator 87 withinpath-based input unit 183 generates an estimated phase from the inputdata stream for each possible transition within the input data stream.For example, given the two states 0 and 1, phase estimator 87 generatesphase estimates for the following four transitions: 0→0; 0→1; 1→0; and1→1. Like branch metric unit 88, phase estimator 87 may use a set ofwell-known predetermined and preprogrammed calculations or it may use avariety of calculations adaptive to several conditions to generate theestimated phase for each transition. Phase estimator 87 may alsoestimate the phase associated with each transition using Equations (12)and (13), as described above.

The phase estimates generated by phase estimator 87 are sent topath-based phase buffer 186. Path-based phase buffer 186 may include adedicated phase buffer for each transition, 0→0, 0→1, 1→0, and 1→1.These dedicated phase buffers hold the most recent phase estimatesgenerated by phase estimator 87 for each transition and may befirst-in-first-out (FIFO) buffers. After the phase estimates generatedby phase estimator 87 are sent to path-based phase buffer 186, phasecalculation unit 187 accesses output unit 95 via link 190 to retrieveinformation on a plurality of transitions in the best surviving path.Using the information on the plurality of transitions in the bestsurviving path, phase calculation unit 187 selects a correspondingestimated phase for each transition in the plurality of transitions fromthe path-based phase buffer 186 and adds them together. The result, amoving sum summed phase 191, is sent to decision unit 184.

Concurrently, path-based threshold unit 182 also receives information ona plurality of transitions in the best surviving path. Path-basedthreshold unit 182 includes threshold table 188 which containstransition-based threshold values for all possible transitions withpositive RI and negative RI. Accordingly, each transition has atransition-based threshold value associated with positive RI and atransition-based threshold value associated with negative RI. Thetransition-based threshold value for each transition is one half of thetheoretical RI phase for that transition under either positive ornegative RI. Threshold table 188 may hold different values for thetransition-based threshold under a PR4 target and under a MFPR4 target.Alternatively, the transition-based threshold value may be calculatednot just using a n-th user bit and a (n−1)-th user bit (i.e., onetransition), but may be calculated using the n-th user bit, the (n−1)-thuser bit, and a (n−2)-th user bit or a (n+1)-th user bit. Thresholdtable 188 is coupled to threshold calculation unit 189 to which it sendsthe transition-based threshold values corresponding to the plurality oftransitions in the best surviving path.

Threshold calculation unit 189 is coupled between path-based thresholdtable 188 and decision unit 184 and receives transition-based thresholdvalues corresponding to the plurality of transitions in the bestsurviving path. Threshold calculation unit 189 separately sums thetransition-based threshold values associated with positive RI and thetransition-based threshold values associated with negative RI togenerate two moving sum summed thresholds 192 that it sends to decisionunit 184.

Decision unit 184 is coupled to threshold calculation unit 189, phasecalculation unit 187, and branch metric selector 92 within input unit91. Decision unit 184 receives summed thresholds 192 from thresholdcalculation unit 189 and summed phase 191 from phase calculation unit187. It compares summed phase 191 against summed thresholds 192 todetermine whether there exists positive RI, negative RI, or no RI. Basedon the comparison, decision unit 184 generates RI flag 101, whichindicates positive RI, negative RI, or no RI. Decision unit 184 suppliesRI flag 101 to branch metric selector 92 within input unit 91. There mayexist an overall pipeline latency between RI flag 101 and the input datasignal at input terminal 90.

It will be understood by one skilled in the art that filter 105,adaptive threshold unit 131, transition-based threshold unit 141, andpath-based threshold unit 182 with path-based input unit 183 may be usedseparately or in combination. For example, filter 105 may be used alone,with adaptive threshold unit 131, with transition-based threshold unit141, with path-based threshold unit 182 with path-based input unit 183,or with both adaptive threshold unit 131 and transition-based thresholdunit 141. Other combinations are possible, for specific applications.FIGS. 12A-S illustrate the BER as a function of the off-track phaseshift with respect to the on-track signal in degrees at varioussignal-to-noise ratios (SNR) for a Viterbi decoder without an RIdetector, a Viterbi decoder with an RI detector and a Viterbi decoderusing filter 105, adaptive threshold unit 131, and transition-basedthreshold unit 141 either alone or in combination.

The systems and methods disclosed herein are not inherently related toany particular computer or other apparatus, and may be implemented by asuitable combination of hardware, software, and/or firmware. Softwareimplementations may include one or more computer programs. A computerprogram is a set of instructions readable and executable by a processorand can be written in any form of programming language, includingcompiled or interpreted languages, and it can be deployed in any form,including as a stand alone program or as a module, component,subroutine, or other unit suitable for use in a computing environment. Acomputer program can be deployed to be executed on one computer or onmultiple computers at one site or distributed across multiple sites andinterconnected by a communication network. Software may also beimplemented as a computer program product, i.e., one or more computerprograms tangibly embodied in an information carrier, e.g., in a machinereadable storage device or in a propagated signal, for execution by, orto control the operation of, data processing apparatus, e.g., aprogrammable processor, a computer, or multiple computers.

The foregoing description is intended to illustrate but not to limit thescope of the invention, which is defined by the scope of the appendedclaims. Other embodiments are within the scope of the following claims.

What is claimed is:
 1. A system for decoding data stored on a datastorage medium, the system comprising: an input unit operative toestimate phases associated with the data; and a decision unit operativeto detect radial incoherence based on the estimated phases.
 2. Thesystem of claim 1 further comprising an adder operative to generate asum by adding a plurality of selected estimated phases, wherein: theinput unit is further operative to select the selected estimated phases,and the decision unit is further operative to generate a flag using thesum, wherein the flag indicates a type of radial incoherence associatedwith the data.
 3. The system of claim 2, wherein the sum is a first sum,further comprising: an add-compare-select unit operative to select atransition from a subset of possible transitions of the data; and atransition-based threshold unit operative to: store a plurality oftransition-based threshold value s; receive the selected transition fromthe add-compare-select unit; select one of the plurality oftransition-based threshold values in response to the selectedtransition; generate a second sum by adding a plurality of the selectedtransition-based threshold values; and supply the second sum to thedecision unit.
 4. The system of claim 3 wherein the decision unitfurther compares the first sum with the second sum to generate the flag.5. The system of claim 1, further comprising an adaptive threshold unitoperative to: generate an adaptive threshold value; store the adaptivethreshold value; receive a flag from the decision unit, wherein the flagindicates a type of radial incoherence associated with the data; comparethe flag with the adaptive threshold value; generate an adjustedadaptive threshold value by adjusting the adaptive threshold value basedupon the comparison; and store the adjusted adaptive threshold value asthe adaptive threshold value.
 6. The system of claim 5 wherein thedecision unit is further operative to compare the first sum with theadjusted adaptive threshold value to generate the flag.
 7. The system ofclaim 5 wherein generating the adjusted adaptive threshold valuecomprises: increasing the adaptive threshold value when the flagindicates no radial incoherence; and decreasing the adaptive thresholdvalue when the flag indicates negative or positive radial incoherence.8. The system of claim 1 further comprising a filter operative to:receive a plurality of flags from the decision unit; store the pluralityof flags; compare the plurality of flags; and generate a radialincoherence-type signal based upon the comparison.
 9. A method fordecoding data stored on a data storage medium, the method comprising:estimating phases associated with the data; and detecting, with adecision unit, radial incoherence based on the estimated phases.
 10. Themethod of claim 9 further comprising: generating, with an adder, a sumby adding a plurality of selected estimated phases, and wherein thedecision unit generates a flag using the sum, and wherein the flagindicates a type of radial incoherence associated with the data.
 11. Themethod of claim 10, wherein the sum is a first sum, further comprising:selecting, with an add-compare-select unit, a transition from a subsetof the possible transitions; and storing, in a transition-basedthreshold unit, a plurality of transition-based threshold values;receiving, at the transition-based threshold unit, the selectedtransition from the add-compare-select unit; selecting, at thetransition-based threshold unit, one of the plurality oftransition-based threshold values in response to the selectedtransition; generating, at the transition-based threshold unit, a secondsum by adding a plurality of the selected transition-based thresholdvalues; and supplying the second sum to the decision unit.
 12. Themethod of claim 11 further comprising comparing, using the decisionunit, the first sum with the second sum to generate the flag.
 13. Themethod of claim 9 further comprising: storing, in an adaptive thresholdunit, an adaptive threshold value; comparing a flag received from thedecision unit with the adaptive threshold value, wherein the flagindicates a type of radial incoherence associated with the data;generating an adjusted adaptive threshold value by adjusting theadaptive threshold value based upon the comparison; and storing theadjusted adaptive threshold value as the adaptive threshold value. 14.The method of claim 11 wherein generating the flag using the decisionunit further comprises comparing the first sum with the adjustedadaptive threshold value.
 15. The method of claim 13 wherein generatingthe adjusted adaptive threshold value comprises: increasing the adaptivethreshold value when the flag indicates no radial incoherence; anddecreasing the adaptive threshold value when the flag indicates negativeor positive radial incoherence.
 16. The method of claim 9 furthercomprising: receiving a flag from the decision unit; storing a pluralityof the flags; comparing the plurality of the flags; and generating aradial incoherence-type signal based upon the comparison.
 17. A systemfor decoding data stored on a data storage medium, the systemcomprising: a path-based input unit operative to generate a sum; and adecision unit operative to use the sum to detect radial incoherenceassociated with the data.
 18. The system of claim 17, wherein the sum isa first sum, the system further comprising: a path-based threshold unitoperative to generate a second sum; an add-compare-select unit operativeto select a transition from a subset of possible transitions in areceived data stream; an output unit operative to generate a decodeddata signal as an output signal; and the path-based input unit, whereinthe path-based input unit is further operative to: generate estimatedphases of the possible transitions; store the estimated phases in aphase buffer; receive a plurality of selected transitions from theoutput unit; select the estimated phases that correspond to theplurality of selected transitions; generate the first sum by adding theestimated phases that correspond to the plurality of selectedtransitions; and supply the first sum to the decision unit.
 19. Thesystem of claim 18 wherein the path-based threshold unit is furtheroperative to: store a plurality of path-based threshold values; receivethe plurality of selected transitions from the output unit; select thepath-based threshold values that correspond to the plurality of selectedtransitions; generate the second sum by adding the selected path-basedthreshold values; and supply the second sum to the decision unit. 20.The system of claim 17 further comprising an adaptive threshold unitoperative to: store an adaptive threshold value; receive a flag from thedecision unit; compare the flag with the adaptive threshold value;generate an adjusted adaptive threshold value by adjusting the adaptivethreshold value based upon the comparison; supply the adjusted adaptivethreshold value to the decision unit; and store the adjusted adaptivethreshold value as the adaptive threshold value.